Lemma 3.3 (Nadkarni [1]})   Let \(S\)  be a free Borel automorphism on a standard Borel space \((X,{\mathcal {B}})\) . Then there exists a countable collection of Borel sets \(\lbrace A\rbrace _{i\in {\mathbb {N}}}\)  such that it generate \({\mathcal {B}}\)  and none of the set in the collection contains a full \(S\) -orbit.

